Assuming unique gapped ground states on finite open chains with boundary fields, the infinite S=1 AF Heisenberg chain is proven to have a nontrivial SPT topological index.
Ogata, A Z2-index of symmetry protected topologi- cal phases with time reversal symmetry for quantum spin chains, Commun
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Develops local diagnostics for strong symmetries and strong-to-weak symmetry breaking via infinite-volume definitions and local charge coherence, introduces von Neumann symmetries, and derives an LSM-type anomaly constraint for quantum spin chains.
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The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
Assuming unique gapped ground states on finite open chains with boundary fields, the infinite S=1 AF Heisenberg chain is proven to have a nontrivial SPT topological index.